MoS2 phononic crystals for advanced thermal management

Effective thermal management of electronic devices encounters substantial challenges owing to the notable power densities involved. Here, we propose layered MoS2 phononic crystals (PnCs) that can effectively reduce thermal conductivity (κ) with relatively small disruption of electrical conductivity (σ), offering a potential thermal management solution for nanoelectronics. These layered PnCs exhibit remarkable efficiency in reducing κ, surpassing that of Si and SiC PnCs with similar periodicity by ~100-fold. Specifically, in suspended MoS2 PnCs, we measure an exceptionally low κ down to 0.1 watts per meter kelvin, below the amorphous limit while preserving the crystalline structure. These findings are supported by molecular dynamics simulations that account for the film thickness, porosity, and temperature. We demonstrate the approach efficiency by fabricating suspended heat-routing structures that effectively confine and guide heat flow in prespecified directions. This study underpins the immense potential of layered materials as directional heat spreaders, thermal insulators, and active components for thermoelectric devices.


Thermal conductivity measurements
Temperature-dependent thermal conductivity: The measurements were performed in a temperature-controlled vacuum chamber (Linkam) where the heatsink temperature varied from 123 K to 473 K.The samples were characterized using the 1LRT.Table S2.Electrical conductivity of FIB-patterned layered MoS2.Rσ = σpristine / σpnc.

MD simulations
Concerning the dependence of the thermal conductivity with the layer thickness, three sizes have been investigated; 4 nm (7 tri-layers), 10 nm (17 tri-layers) and a bulk system at 300 K as presented in Figure 3.It should be noted that even for 10 nm thickness, the bulk conductivity has not been reached in contrast to ref (58) which claims that the thermal conductivity has already reached that of bulk values from 3 tri-layers onwards (about 1.8 nm).The discrepancy is based on the fact that in the present study, the well-established EMD method is used extensively (averaging the results of 10 different cases having random initial distribution of atomic velocities) while in ref (58) the authors have used the homogeneous nonequilibrium MD (HNEMD) method (59,60) in the recently developed form, which is constructed in order for the HNEMD method to become efficient for general many-body potentials, including the REBO potential (61).The current outcome using the EMD method supports the validity of the aforementioned methodology in combination with the selected interatomic potential owing to the agreement with the experimental results.S3.Thickness dependence of thermal conductivity of MoS2 membranes.
For the main focus of our work, we scaled down the porous, thin film for computational optimization, to study its thermal conductivity.Table S3 shows information about the original pristine system and the scaled down system that we studied.To make sure the scaled down system is acceptable for our simulation, we took into account the phonon means free path (PMFP).The crystalline surface of the system should be large enough, so it does not restrict the phononic vibrations.Therefore, the smallest path between two consecutive holes is equal to the periodicity minus the hole diameter.This smallest path evaluates to 62.4 nm which is larger than the PMFP = 41 nm and hence, the scale down of the system does not restrict the thermal conductivity in any way.The in-plane thermal conductivity was calculated to be equal to 5.2 W/mK which compares well with our experimental results.

Fig. S2 .
Fig. S2.SEM image of a typical MoS2 PnC membrane.The unpatterned central region was used as heating island for the thermal measurements.

Fig. S3 .
Fig. S3.TEM images of the patterned 4.5 nm thick MoS2 membrane.(a) shows the morphology of a typical PnC.(b), (c), and (d) respectively show the corresponding regions in the red, blue, and green boxes in (a).The results indicate that the areas away from the holes are crystalline, and the lattice dimensions remain unchanged.

Fig. S5 .
Fig. S5.Thickness-dependent dimensions of PnCs.(a) Schematic diagram of the MoS2 PnCs, a is the period, n is the neck size, nc is the neck size without the amorphous region, d is the hole diameter, and na is the size of the amorphous region.(b) Variation of each parameter shown in (a) with respect to membrane thickness while keeping FIB processing conditions at 30kV and 2pA.

Fig. S6 .
Fig. S6.STEM images (a and c) and high-angle annular dark-field (HAADF) imaging profiles and gallium atom trace (b and d) for MoS2 patterned samples with thicknesses of 40 nm (a and b) and 4.5 nm (c and d).

Fig. S8 .
Fig. S8.Thermal conductivity measurements of MoS2 PnCs.(a-d) Thermal conductivity of the 4.5 nm-thick, free-standing pristine and nanopatterned MoS2 membranes measured by 2LRT.(a) Background and Heating scans of pristine MoS2 suspended film.These scans were measured using a probe laser (532 nm) with an incident power Pprobe ~10 µW, and a heating laser (405 nm) with an absorbed power of Ppump = 137.5 µW.The heating laser was focused onto the center of the sample (r = 0 µm) for the heating scans.(b) Background and Heating scans of MoS2 PnCs suspended film.These scans were measured using a probe laser with an incident power of Pprobe ~6.8 µW, and a heating laser with an absorbed power of Ppump = 15.8 µW.(c) Temperature profile on the sample, extracted from (a), and (d) shows the corresponding

Fig. S9 .
Fig. S9.Thermal conductivity reduction factor of nanopatterned MoS2 as a function of the membrane thickness.

3 .
Fig. S10.Electrical conductivity measurement of nanopatterned MoS2.(a) Optical image of a typical MoS2 device.(b) and (c) SEM images of (a) and PnC in the patterned region in (b), respectively.

Fig. S11 .
Fig. S11.Optical images of (a) pristine and (b) nanopatterned MoS2.(c) A1g Raman frequency with and without heating as a function of position.(d) A1g Raman peak intensity as a function of position.

Fig. S14 .
Fig. S14.Normalized accumulated thermal conductivity as a function of the phonon MFP. Table

Table S4 .
Values of the sample parameters and the scaled down values used in the MD simulation.